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Astronomical image segmentation by self-organizing neural networks and wavelets

NEURAL NETWORKS 2003年第3-4期16卷 411-417页

作者： Núñez, J Llacer, J Univ Barcelona Dept Astron & Meteorol E-08028 Barcelona Spain Observ Fabra Barcelona Spain EC Engn Consultants LLC Los Gatos CA 95032 USA

Standard image segmentation methods may not be able to segment astronomical images because their special nature. We present an algorithm for astronomical image segmentation based on self-organizing neural networks and wavelets. We begin by performing wavelet decomposition of the image. The segmentation process has two steps. In the first we separate the stars and other prominent objects using the second plane (w(2)) of the wavelet decomposition, which has little noise but retains enough signal to represent those objects. This method was as least as effective as the traditional source extraction methods in isolating bright objects both from the background and from extended sources. In the second step the rest of the image (extended sources and background) is segmented using a self-organizing neural network. The result is a predetermined number of clusters, which we associate with extended regions plus a small region for each star or bright object. We have applied the algorithm to segment images of both galaxies and planets. The results show that the simultaneous use of all the scales in the self-organizing neural network helps the segmentation process, since it takes into account not only the intensity level, but also both the high and low frequencies present in the image. The connectivity of the regions obtained also shows that the algorithm is robust in the presence of noise. The method can also be applied to restored images. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： image segmentation neural networks self-organizing NN wavelets a trous algorithm image processing HST images

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Adaptive wavelet transform algorithm for image compression applications

Adaptive wavelet transform algorithm for image compression a...

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Conference on applications of Digital image processing xxVI

作者： Pogrebnyak, O Ramírez, PM Inst Politecn Nacl CIC Mexico City 07738 DF Mexico

ISBN: (纸本)0819450766

A new algorithm of locally adaptive wavelet transform is presented. The algorithm implements the integer-to-integer lifting scheme. It performs an adaptation of the wavelet function at the prediction stage to the local image data activity. The proposed algorithm is based on the generalized framework for the lifting scheme that permits to obtain easily different wavelet coefficients in the case of the ((N) over tilde , N) lifting. It is proposed to perform the hard switching between (2, 4) and (4, 4) lifting filter outputs according to an estimate of the local data activity. When the data activity is high, i.e.. in the vicinity of edges, the (4, 4) lifting is performed. Otherwise. in the plain areas. the (2,4) decomposition coefficients are calculated. The calculations are rather simples that permit the implementation of the designed algorithm in fixed point DSP processors. The proposed adaptive transform possesses the perfect restoration of the processed data and possesses good energy compactation. The designed algorithm was tested on different images. The proposed adaptive transform algorithm can be used for image/signal compression and noise suppression.

关键词： image processing wavelets lifting scheme lossless compression

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Multiscale statistical image models and Bayesian methods

Multiscale statistical image models and Bayesian methods

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Conference on Wavelet applications in Industrial processing

作者： Pizurica, A Philips, W Univ Ghent Dept Telecommun & Informat Proc B-9000 Ghent Belgium

ISBN: (纸本)0819451541

Multiscale statistical signal and image models resulted in major advances in many signal processing disciplines. This paper focuses on Bayesian image denoising. We discuss two important problems in specifying priors for image wavelet coefficients. The first problem is the characterization of the marginal subband statistics. Different existing models include highly kurtotic heavy-tailed distributions, Gaussian scale mixture models and weighted sums of two different distributions. We discuss the choice of a particular prior and give some new insights in this problem. The second problem that we address is statistical modelling of inter- and intrascale dependencies between image wavelet coefficients. Here we discuss the use of Hidden Markov Tree models, which are efficient in capturing inter-scale dependencies, as well as the use of Markov Random Field models, which are more efficient when it comes to spatial (intrascale) correlations. Apart from these relatively complex models, we review within a new unifying framework a class of low-complexity locally adaptive methods, which encounter the coefficient dependencies via local spatial activity indicators.

关键词： wavelets Bayesian estimation Markov Random Field models. hidden Markov Tree models

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A new video coder based on second generation wavelets

A new video coder based on second generation wavelets

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Proceedings: 2003 International Conference on image processing, ICIP-2003

作者： Brangoulo, Sébastien Gioia, Patrick Laurent, Nathalie Fournier, Jérôme France Telecom R and D 4 Rue du Clos Courtel 35512 Cesson-Sevigne Cedex France

We consider a new way to encode video sequences. The proposed method is based on Second Generation wavelets (SGW), a novel mathematic transform, successfully applied in 3D coding. This video coder is created by combining the wavelet theory and mesh geometry. With this and the SGW, we will be able to apply onto the video image, the mathematical transform to locate and to encode the error, results of the motion compensation process. This powerful signal processing theory allows a very well adapted coding of high frequencies. The main advantage is that these wavelets can be designed to fit exactly on singularities, shapes, textures, and edges. Hence, we can reduce redundancy and improve considerably coding efficiency over those peculiar settings. This new coder can be applied on all classical applications, such as very low bit rate transmissions, video streaming, visio conference and video on demand.

关键词： image coding

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Wavelet-based signal modeling and processing algorithms with applications

Wavelet-based signal modeling and processing algorithms with...

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作者： Wan, Yi Rice University

学位级别：Ph.D.

Good signal representation and the corresponding signal processing algorithms lie at the heart of the signal processing research effort. Since the 1980's wavelet analysis has become more and more a mature tool in many applications such as image compression due to some key advantages over the traditional Fourier analysis. In this thesis we first develop a wavelet-based statistical framework and an efficient algorithm for solving the linear inverse problems with application to image restoration. The result is an efficient method that produces state-of-the-art results for such problems and has potential further applications in other areas. To overcome the issues such as the blocking artifacts in using orthogonal wavelets, we next investigate the design issue of more flexible basis representations based on frames. In particular, we develop a quasi image rotation method that is based on pixel reassignment and hence retains the original image statistics. When combined with translation operators, this method provides very efficient and desirable frames for image processing. Given a frame, due to the large number of redundant basis functions in it, how to efficiently implement a frame-based algorithm is the key issue. We show this through the example of optimal signal denoising in the presence of added zero-mean white noise. We show that the optimal solution exists yet the computation toward the solution is very heavy. We develop a framework that allows for fast approximations to the optimal solution and has clear physical interpretation. This method is in essence different from the other various approximate approaches such the basis pursuit and has applications in other areas such as image segmentation. We also develop a complexity regularized iterative algorithm for getting sparse solutions to the frame-based signal denoising problem.

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The zero-rate spread-spectrum watermarking game

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IEEE TRANSACTIONS ON signal processing 2003年第4期51卷 1098-1117页

作者： Moulin, P Ivanovic, A Univ Illinois Beckman Inst Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

This paper develops a game-theoretic methodology to design and embed M messages in signals and images in the presence of an adversary. Here, M is assumed to be subexponential in the signal's sample size (zero-rate transmission), and the embedding is done using spread-spectrum watermarking. The detector performs statistical hypothesis testing. The system is designed to minimize probability of error under the worst-case attack in a prescribed class of attacks. The variables in this game are probability distributions for the watermarker and attacker. Analytical solutions are derived under the assumption of Gaussian host vectors, watermarks and attacks, and squared-error distortion constraints for the watermarker and the attacker. The Karhunen-Loeve transform (KLT) plays a central role in this study. The optimal distributions for the watermarker and the attacker are Gaussian test channels applied to the KLT coefficients;the game is then reduced to a maxmin power-allocation problem between the channels. As a byproduct of this analysis, we can determine the optimal tradeoff between using the most efficient (in terms of detection performance) signal components for transmission and spreading the transmission across many components (to fool the attacker's attempts to eliminate the watermark). We also conclude that in this framework, additive watermarks are suboptimal;they are, however, nearly optimal in a small-distortion regime. The theory is applied to watermarking of autoregressive processes and to wavelet-based image watermarking. The optimal watermark design outperforms conventional designs based on heuristic power allocations and/or simple correlation detectors.

关键词： autoregressive processes image processing Karhunen-Loeve transform maximum a posteriori detection minmax optimization random codes visual perception watermarking wavelets

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Interferometric side scan sonar signal denoised by wavelets

Interferometric side scan sonar signal denoised by wavelets

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Conference on Independent Component Analyses, wavelets, and Neural Networks

作者： Sintes, C Legris, M Solaiman, B ENST Bretagne F-29285 Brest France

ISBN: (纸本)0819449628

This paper concerns the possibilities that side scan sonar have to determine the bathymetry. New side scan sonars, which are able to image the sea bottom with a high definition, estimate the relief with the same definition as conventional sonar, images, using an interferometric multisensors system. Drawbacks concern the accuracy and errors of the numerical altitude model. Interferometric methods use a phase difference to determine a time delay between two sensors. The phase difference belongs to a finite interval ]-pi, +pi], but the time delay between two sensors does not belong to a finite interval : the phase is 2pi biased. The used sonar is designed for the use of the vernier technique, which allows to remove this bias. The difficulty comes from interferometric noise, which generates errors on the 2pi bias estimation derived from the vernier. The traditional way to reduce noise impact on the interferometric signal, is to average data. This method does not preserve the resolution of the bathymetric estimation. This paper presents an attempt to improve the accuracy and resolution of the interferometric signal through a wavelets based method of image despecklisation. Traditionally, despecklisation is processed on the logarithm of absolute value of the signal. But for this application, the proposed interferometric despecklisation is achieved directly on the interferometric signal by integrating information, guided by the despeckled image. Finally, this multiscale analysis corresponds to an auto adaptive average filtering. A variant of this method is introduced and based on this assumption. This method used the identity function to reconstruct the signal. On the presented results, phase despecklisation improves considerably the quality of the interferometric signal in term of signal to noise ratio, without an important degradation of resolution.

关键词： Interferometry wavelets signal processing image filtering image fusion Interference (communication) Digital filtering Electronic filtering Linear filtering Sensors

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Unified approach for constructing multiwavelets with approximation order using refinable super-functions

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IEE PROCEEDINGS-VISION image AND signal processing 2003年第3期150卷 143-152页

作者： Özkaramanli, H Eastern Mediterranean Univ Dept Elect & Elect Engn Magosa Turkey

A unified approach for constructing a large class of multiwavelets is presented. This class includes Geronimo-Hardin-Massopust, Alpert, finite element and Daubechies-like multiwavelets. The approach is based on the characterisation of approximation order of r multiscaling functions using a known compactly supported refinable super-function. The characterisation is formulated as a generalised eigenvalue equation. The generalised left eigenvectors of the finite down-sampled convolution matrix L-f give the coefficients in the finite linear combination of multiscaling functions that produce the desired super-function. The unified approach based on the super-function theory can be used to construct new multiwavelets with short support, high approximation order and symmetry.

关键词： .orthogonality multiwavelets functions and wavelets characterised refinable super-functions Strang and Strela matrix sum refinement mask multiscaling function

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Multiscalegeometric image processing

Multiscalegeometric image processing

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作者： Justin K. Romberg Rice University

学位级别：博士

Since their introduction a little more than 10 years ago, wavelets have revolutionized image processing. Wavelet based algorithms define the state-of-the-art for applications including image coding (JPEG-2000), restoration, and segmentation. Despite their success, wavelets have significant shortcomings in their treatment of edges. wavelets do not parsimoniously capture even the simplest geometrical structure in images, and wavelet based processing algorithms often produce images with ringing around the edges. As a first step towards accounting for this structure, we will show how to explicitly capture the geometric regularity of contours in cartoon images using the wedgelet representation and a multiscale geometry model. The wedgelet representation builds up an image out of simple piecewise constant functions with linear discontinuities. We will show how the geometry model, by putting a joint distribution on the orientations of the linear discontinuities, allows us to weigh several factors when choosing the wedgelet representation: the error between the representation and the original image, the parsimony of the representation, and whether the wedgelets in the representation form "natural" geometrical structures. We will analyze a simple wedgelet coder based on these principles, and show that it has optimal asymptotic performance for simple cartoon images. Next, we turn our attention to piecewise smooth images; images that are smooth away from a smooth contour. Using a representation composed of wavelets and wedgeprints (wedgelets projected into the wavelet domain), we develop a quadtree based prototype coder whose rate-distortion performance is asymptotically near-optimal. We use these ideas to implement a full-scale image coder that outperforms JPEG-2000 both in peak signal to noise ratio (by 1--1.5dB at low bitrates) and visually. Finally, we shift our focus to building a statistical image model directly in the wavelet domain. For applications other than compress

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Wavelet footprints: Theory, algorithms, and applications

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IEEE TRANSACTIONS ON signal processing 2003年第5期51卷 1306-1323页

作者： Dragotti, PL Vetterli, M Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London England Swiss Fed Inst Technol Audio Visual Commun Lab CH-1015 Lausanne Switzerland Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA

In recent years', wavelet-based algorithms have been successful in different signal processing. tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. In this paper, we study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing that any piecewise smooth signal can be expressed as a sum. of a piecewise polynomial signal and a uniformly smooth residual (see Theorem 1 in Section II). We then introduce the notion of footprints, which are scale space vectors that model discontinuities in piecewise polynomial signals exactly. We show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints. This also leads to efficient approximation of piecewise smooth functions. Finally, we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising, compression, and (nonblind) deconvolution. In the case of compression, we also prove that at high rates, footprint-based algorithms attain optimal performance (see Theorem 3 in Section V).

关键词： compression denoising matching pursuit non-linear approximation wavelets

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